def test_hfft(self):
x = random(14) + 1j*random(14)
x_herm = np.concatenate((random(1), x, random(1)))
x = np.concatenate((x_herm, x[::-1].conj()))
assert_array_almost_equal(np.fft.fft(x), np.fft.hfft(x_herm))
assert_array_almost_equal(np.fft.hfft(x_herm) / np.sqrt(30),
np.fft.hfft(x_herm, norm="ortho"))
def test_simple(self):
x = np.array([[-.5, .5, 1.5], [-.5, 1.5, 2.5], [-.5, 2.5, .5],
[.5, .5, 1.5], [.5, 1.5, 2.5], [.5, 2.5, 2.5]])
H, edges = histogramdd(x, (2, 3, 3), range=[[-1, 1], [0, 3], [0, 3]])
answer = np.array([[[0, 1, 0], [0, 0, 1], [1, 0, 0]],
[[0, 1, 0], [0, 0, 1], [0, 0, 1]]])
assert_array_equal(H, answer)
# Check normalization
ed = [[-2, 0, 2], [0, 1, 2, 3], [0, 1, 2, 3]]
H, edges = histogramdd(x, bins=ed, density=True)
assert_(np.all(H == answer / 12.))
# Check that H has the correct shape.
H, edges = histogramdd(x, (2, 3, 4),
range=[[-1, 1], [0, 3], [0, 4]],
density=True)
answer = np.array([[[0, 1, 0, 0], [0, 0, 1, 0], [1, 0, 0, 0]],
[[0, 1, 0, 0], [0, 0, 1, 0], [0, 0, 1, 0]]])
assert_array_almost_equal(H, answer / 6., 4)
# Check that a sequence of arrays is accepted and H has the correct
# shape.
z = [np.squeeze(y) for y in np.split(x, 3, axis=1)]
H, edges = histogramdd(z,
bins=(4, 3, 2),
range=[[-2, 2], [0, 3], [0, 2]])
answer = np.array([[[0, 0], [0, 0], [0, 0]], [[0, 1], [0, 0], [1, 0]],
[[0, 1], [0, 0], [0, 0]], [[0, 0], [0, 0], [0, 0]]])
assert_array_equal(H, answer)
Z = np.zeros((5, 5, 5))
Z[list(range(5)), list(range(5)), list(range(5))] = 1.
H, edges = histogramdd([np.arange(5), np.arange(5), np.arange(5)], 5)
assert_array_equal(H, Z)
def test_ifftn(self):
x = random((30, 20, 10)) + 1j*random((30, 20, 10))
assert_array_almost_equal(
np.fft.ifft(np.fft.ifft(np.fft.ifft(x, axis=2), axis=1), axis=0),
np.fft.ifftn(x))
assert_array_almost_equal(np.fft.ifftn(x) * np.sqrt(30 * 20 * 10),
np.fft.ifftn(x, norm="ortho"))
def test_density(self):
x = array([1, 2, 3, 1, 2, 3, 1, 2, 3])
y = array([1, 1, 1, 2, 2, 2, 3, 3, 3])
H, xed, yed = histogram2d(x,
y, [[1, 2, 3, 5], [1, 2, 3, 5]],
density=True)
answer = array([[1, 1, .5], [1, 1, .5], [.5, .5, .25]]) / 9.
assert_array_almost_equal(H, answer, 3)
def test_svd_build(self):
# Ticket 627.
a = array([[0., 1.], [1., 1.], [2., 1.], [3., 1.]])
m, n = a.shape
u, s, vh = linalg.svd(a)
b = dot(transpose(u[:, n:]), a)
assert_array_almost_equal(b, np.zeros((2, 2)))
def test_rfft(self):
x = random(30)
for n in [x.size, 2*x.size]:
for norm in [None, 'ortho']:
assert_array_almost_equal(
np.fft.fft(x, n=n, norm=norm)[:(n//2 + 1)],
np.fft.rfft(x, n=n, norm=norm))
assert_array_almost_equal(np.fft.rfft(x, n=n) / np.sqrt(n),
np.fft.rfft(x, n=n, norm="ortho"))
def test_eigh_build(self):
# Ticket 662.
rvals = [68.60568999, 89.57756725, 106.67185574]
cov = array([[77.70273908, 3.51489954, 15.64602427],
[3.51489954, 88.97013878, -1.07431931],
[15.64602427, -1.07431931, 98.18223512]])
vals, vecs = linalg.eigh(cov)
assert_array_almost_equal(vals, rvals)
def test_equal_nan_default(self):
# Make sure equal_nan default behavior remains unchanged. (All
# of these functions use assert_array_compare under the hood.)
# None of these should raise.
a = np.array([np.nan])
b = np.array([np.nan])
assert_array_equal(a, b)
assert_array_almost_equal(a, b)
assert_array_less(a, b)
assert_allclose(a, b)
def test_lstsq_complex_larger_rhs(self):
# gh-9891
size = 20
n_rhs = 70
G = np.random.randn(size, size) + 1j * np.random.randn(size, size)
u = np.random.randn(size, n_rhs) + 1j * np.random.randn(size, n_rhs)
b = G.dot(u)
# This should work without segmentation fault.
u_lstsq, res, rank, sv = linalg.lstsq(G, b, rcond=None)
# check results just in case
assert_array_almost_equal(u_lstsq, u)
def test_asym(self):
x = array([1, 1, 2, 3, 4, 4, 4, 5])
y = array([1, 3, 2, 0, 1, 2, 3, 4])
H, xed, yed = histogram2d(x,
y, (6, 5),
range=[[0, 6], [0, 5]],
density=True)
answer = array([[0., 0, 0, 0, 0], [0, 1, 0, 1, 0], [0, 0, 1, 0, 0],
[1, 0, 0, 0, 0], [0, 1, 1, 1, 0], [0, 0, 0, 0, 1]])
assert_array_almost_equal(H, answer / 8., 3)
assert_array_equal(xed, np.linspace(0, 6, 7))
assert_array_equal(yed, np.linspace(0, 5, 6))
def test_weights(self):
v = np.random.rand(100)
w = np.ones(100) * 5
a, b = histogram(v)
na, nb = histogram(v, density=True)
wa, wb = histogram(v, weights=w)
nwa, nwb = histogram(v, weights=w, density=True)
assert_array_almost_equal(a * 5, wa)
assert_array_almost_equal(na, nwa)
# Check weights are properly applied.
v = np.linspace(0, 10, 10)
w = np.concatenate((np.zeros(5), np.ones(5)))
wa, wb = histogram(v, bins=np.arange(11), weights=w)
assert_array_almost_equal(wa, w)
# Check with integer weights
wa, wb = histogram([1, 2, 2, 4], bins=4, weights=[4, 3, 2, 1])
assert_array_equal(wa, [4, 5, 0, 1])
wa, wb = histogram([1, 2, 2, 4],
bins=4,
weights=[4, 3, 2, 1],
density=True)
assert_array_almost_equal(wa, np.array([4, 5, 0, 1]) / 10. / 3. * 4)
# Check weights with non-uniform bin widths
a, b = histogram(np.arange(9), [0, 1, 3, 6, 10],
weights=[2, 1, 1, 1, 1, 1, 1, 1, 1],
density=True)
assert_almost_equal(a, [.2, .1, .1, .075])
def test_exotic_weights(self):
# Test the use of weights that are not integer or floats, but e.g.
# complex numbers or object types.
# Complex weights
values = np.array([1.3, 2.5, 2.3])
weights = np.array([1, -1, 2]) + 1j * np.array([2, 1, 2])
# Check with custom bins
wa, wb = histogram(values, bins=[0, 2, 3], weights=weights)
assert_array_almost_equal(wa, np.array([1, 1]) + 1j * np.array([2, 3]))
# Check with even bins
wa, wb = histogram(values, bins=2, range=[1, 3], weights=weights)
assert_array_almost_equal(wa, np.array([1, 1]) + 1j * np.array([2, 3]))
# Decimal weights
from decimal import Decimal
values = np.array([1.3, 2.5, 2.3])
weights = np.array([Decimal(1), Decimal(2), Decimal(3)])
# Check with custom bins
wa, wb = histogram(values, bins=[0, 2, 3], weights=weights)
assert_array_almost_equal(wa, [Decimal(1), Decimal(5)])
# Check with even bins
wa, wb = histogram(values, bins=2, range=[1, 3], weights=weights)
assert_array_almost_equal(wa, [Decimal(1), Decimal(5)])
def test_eig_build(self):
# Ticket #652
rva = array([
1.03221168e+02 + 0.j, -1.91843603e+01 + 0.j,
-6.04004526e-01 + 15.84422474j, -6.04004526e-01 - 15.84422474j,
-1.13692929e+01 + 0.j, -6.57612485e-01 + 10.41755503j,
-6.57612485e-01 - 10.41755503j, 1.82126812e+01 + 0.j,
1.06011014e+01 + 0.j, 7.80732773e+00 + 0.j, -7.65390898e-01 + 0.j,
1.51971555e-15 + 0.j, -1.51308713e-15 + 0.j
])
a = arange(13 * 13, dtype=float64)
a.shape = (13, 13)
a = a % 17
va, ve = linalg.eig(a)
va.sort()
rva.sort()
assert_array_almost_equal(va, rva)
def test_all_1d_norm_preserving(self):
# verify that round-trip transforms are norm-preserving
x = random(30)
x_norm = np.linalg.norm(x)
n = x.size * 2
func_pairs = [(np.fft.fft, np.fft.ifft),
(np.fft.rfft, np.fft.irfft),
# hfft: order so the first function takes x.size samples
# (necessary for comparison to x_norm above)
(np.fft.ihfft, np.fft.hfft),
]
for forw, back in func_pairs:
for n in [x.size, 2*x.size]:
for norm in [None, 'ortho']:
tmp = forw(x, n=n, norm=norm)
tmp = back(tmp, n=n, norm=norm)
assert_array_almost_equal(x_norm,
np.linalg.norm(tmp))
def test_polyfit_build(self):
# Ticket #628
ref = [-1.06123820e-06, 5.70886914e-04, -1.13822012e-01,
9.95368241e+00, -3.14526520e+02]
x = [90, 91, 92, 93, 94, 95, 96, 97, 98, 99, 100, 101, 102, 103,
104, 105, 106, 107, 108, 109, 110, 111, 112, 113, 114, 115,
116, 117, 118, 119, 120, 121, 122, 123, 124, 125, 126, 129,
130, 131, 132, 133, 134, 135, 136, 137, 138, 139, 140, 141,
146, 147, 148, 149, 150, 151, 152, 153, 154, 155, 156, 157,
158, 159, 160, 161, 162, 163, 164, 165, 166, 167, 168, 169,
170, 171, 172, 173, 174, 175, 176]
y = [9.0, 3.0, 7.0, 4.0, 4.0, 8.0, 6.0, 11.0, 9.0, 8.0, 11.0, 5.0,
6.0, 5.0, 9.0, 8.0, 6.0, 10.0, 6.0, 10.0, 7.0, 6.0, 6.0, 6.0,
13.0, 4.0, 9.0, 11.0, 4.0, 5.0, 8.0, 5.0, 7.0, 7.0, 6.0, 12.0,
7.0, 7.0, 9.0, 4.0, 12.0, 6.0, 6.0, 4.0, 3.0, 9.0, 8.0, 8.0,
6.0, 7.0, 9.0, 10.0, 6.0, 8.0, 4.0, 7.0, 7.0, 10.0, 8.0, 8.0,
6.0, 3.0, 8.0, 4.0, 5.0, 7.0, 8.0, 6.0, 6.0, 4.0, 12.0, 9.0,
8.0, 8.0, 8.0, 6.0, 7.0, 4.0, 4.0, 5.0, 7.0]
tested = np.polyfit(x, y, 4)
assert_array_almost_equal(ref, tested)
def test_nd(self):
c = mgrid[-1:1:10j, -2:2:10j]
d = mgrid[-1:1:0.1, -2:2:0.2]
assert_(c.shape == (2, 10, 10))
assert_(d.shape == (2, 20, 20))
assert_array_equal(c[0][0, :], -np.ones(10, 'd'))
assert_array_equal(c[1][:, 0], -2*np.ones(10, 'd'))
assert_array_almost_equal(c[0][-1, :], np.ones(10, 'd'), 11)
assert_array_almost_equal(c[1][:, -1], 2*np.ones(10, 'd'), 11)
assert_array_almost_equal(d[0, 1, :] - d[0, 0, :],
0.1*np.ones(20, 'd'), 11)
assert_array_almost_equal(d[1, :, 1] - d[1, :, 0],
0.2*np.ones(20, 'd'), 11)
def test_poly(self):
assert_array_almost_equal(np.poly([3, -np.sqrt(2), np.sqrt(2)]),
[1, -3, -2, 6])
# From matlab docs
A = [[1, 2, 3], [4, 5, 6], [7, 8, 0]]
assert_array_almost_equal(np.poly(A), [1, -6, -72, -27])
# Should produce real output for perfect conjugates
assert_(np.isrealobj(np.poly([+1.082j, +2.613j, -2.613j, -1.082j])))
assert_(np.isrealobj(np.poly([0+1j, -0+-1j, 1+2j,
1-2j, 1.+3.5j, 1-3.5j])))
assert_(np.isrealobj(np.poly([1j, -1j, 1+2j, 1-2j, 1+3j, 1-3.j])))
assert_(np.isrealobj(np.poly([1j, -1j, 1+2j, 1-2j])))
assert_(np.isrealobj(np.poly([1j, -1j, 2j, -2j])))
assert_(np.isrealobj(np.poly([1j, -1j])))
assert_(np.isrealobj(np.poly([1, -1])))
assert_(np.iscomplexobj(np.poly([1j, -1.0000001j])))
np.random.seed(42)
a = np.random.randn(100) + 1j*np.random.randn(100)
assert_(np.isrealobj(np.poly(np.concatenate((a, np.conjugate(a))))))
def test_pow(self):
"""Test raising a matrix to an integer power works as expected."""
m = matrix("1. 2.; 3. 4.")
m2 = m.copy()
m2 **= 2
mi = m.copy()
mi **= -1
m4 = m2.copy()
m4 **= 2
assert_array_almost_equal(m2, m**2)
assert_array_almost_equal(m4, np.dot(m2, m2))
assert_array_almost_equal(np.dot(mi, m), np.eye(2))
def test_scalar_type_pow(self):
m = matrix([[1, 2], [3, 4]])
for scalar_t in [np.int8, np.uint8]:
two = scalar_t(2)
assert_array_almost_equal(m**2, m**two)
def test_fft(self):
x = random(30) + 1j*random(30)
assert_array_almost_equal(fft1(x), np.fft.fft(x))
assert_array_almost_equal(fft1(x) / np.sqrt(30),
np.fft.fft(x, norm="ortho"))
def test_linspace_equivalence(self):
y, st = np.linspace(2, 10, retstep=1)
assert_almost_equal(st, 8/49.0)
assert_array_almost_equal(y, mgrid[2:10:50j], 13)
def test_irfft2(self):
x = random((30, 20))
assert_array_almost_equal(x, np.fft.irfft2(np.fft.rfft2(x)))
assert_array_almost_equal(
x, np.fft.irfft2(np.fft.rfft2(x, norm="ortho"), norm="ortho"))
def test_ifft(self):
x = random(30) + 1j*random(30)
assert_array_almost_equal(x, np.fft.ifft(np.fft.fft(x)))
assert_array_almost_equal(
x, np.fft.ifft(np.fft.fft(x, norm="ortho"), norm="ortho"))
def test_fft2(self):
x = random((30, 20)) + 1j*random((30, 20))
assert_array_almost_equal(np.fft.fft(np.fft.fft(x, axis=1), axis=0),
np.fft.fft2(x))
assert_array_almost_equal(np.fft.fft2(x) / np.sqrt(30 * 20),
np.fft.fft2(x, norm="ortho"))
def test_rfft2(self):
x = random((30, 20))
assert_array_almost_equal(np.fft.fft2(x)[:, :11], np.fft.rfft2(x))
assert_array_almost_equal(np.fft.rfft2(x) / np.sqrt(30 * 20),
np.fft.rfft2(x, norm="ortho"))
def test_no_side_effects(self):
# This is a regression test that ensures that values passed to
# ``histogram`` are unchanged.
values = np.array([1.3, 2.5, 2.3])
np.histogram(values, range=[-10, 10], bins=100)
assert_array_almost_equal(values, [1.3, 2.5, 2.3])
